Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.5 Higher Derivatives - Exercises - Page 135: 20



Work Step by Step

Since $ f(t)=6t^{9}-2t^5$, then $$\frac{d f}{d t}=54 t^{8}-10t^4, \quad \frac{d^2 f}{d t^2}=432 t^{7}-40t^3, \quad \frac{d^3 f}{d t^3}=3024t^{6}-120t^2 .$$ Hence, $ \frac{d^4 f}{d t^4}=18144 t^{5}-240t, \quad \left.\frac{d^{4} f}{d t^{4}}\right|_{t=1}=17904 $.
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